Cardiac mapping is used to locate aberrant electrical pathways and currents within the heart, as well as mechanical and other aspects of cardiac activity. Various methods and devices have been described for mapping the heart. Such methods and device are described, for example, in U.S. Pat. Nos. 5,471,982 and 5,391,199 and in PCT patent publications WO94/06349, WO96/05768 and WO97/24981. U.S. Pat. No. 5,391,199, for example, describes a catheter including both electrodes for sensing cardiac electrical activity and miniature coils for determining the position of the catheter relative to an externally-applied magnetic field. Using this catheter a cardiologist may collect a set of sampled points within a short period of time, by determining the electrical activity at a plurality of locations and determining the spatial coordinates of the locations.
In order to allow the surgeon to appreciate the determined data, a map, preferably a three dimensional (3D) map, including the sampled points is produced. U.S. Pat. No. 5,391,199 suggests superimposing the map on an image of the heart. The positions of the locations are determined with respect to a frame of reference of the image. However, it is not always desirable to acquire an image, nor is it generally possible to acquire an image in which the positions of the locations can be found with sufficient accuracy.
Various methods are known in the art for reconstructing a 3D map of a cavity or volume using the known position coordinates of a plurality of locations on the surface of the cavity or volume. Some methods include triangulation, in which the map is formed of a plurality of triangles which connect the sampled points. In some cases a convex hull or an alpha-hull of the points is constructed to form the mesh, and thereafter the constructed mesh is shrunk down to fit on the sampled points within the hull. Triangulation methods do not provide a smooth surface and therefore require additional stages of smoothing.
Another method which has been suggested is forming a bounding ellipsoid which encloses the sampled points. The sampled points are projected onto the ellipsoid, and the projected points are connected by a triangulation method. The triangles are thereafter moved with the sampled points back to their original locations, forming a crude piecewise linear approximation of the sampled surface. However, this method may reconstruct only surfaces which have a star shape, i.e., a straight line connecting a center of the reconstructed mesh to any point on the surface does not intersect the surface. In most cases heart chambers do not have a star shape.
In addition, reconstruction methods known in the art require a relatively large number of sampled locations to achieve a suitable reconstructed map. These methods were developed, for example, to work with CT and MRI imaging systems which provide large numbers of points, and therefore generally work properly only on large numbers of points. In contrast, determining the data at the locations using an invasive catheter is a time-consuming process which should be kept as short as possible, especially when dealing with a human heart. Therefore, reconstruction methods which require a large number of determined locations are not suitable.